Black Hole Entropy and String Theory

This is an expanded version of a talk given at “IInd Recontre du Vietnam” held at Ho Chi Minh City in October, 1995. We discuss several aspects of black hole entropy in string theory. We first explain why the geometric entropy in two dimensional noncritical string theory is nonperturbatively finite. We then explain the philosophy of regarding massive string states as black branes and how the BeckensteinHawking entropy for extremal BPS black holes may be understood as coming from degeneracy of string states. This is then discussed in the context of D-strings in Type IIB superstrings. We then describe non-BPS excitations of D-strings and their entropy and explore the possibility that their decay describes Hawking radiation. For these D-strings and other D-branes the entropy and temperature are consequences of the physical motion of stuck open strings along the D-brane and this leads to a simple space-time interpretation. Finally we speculate that the horizon may be itself regarded as a D-brane. In this contribution I will discuss some aspects of black hole entropy and how string theory has helped us to understand this rather mysterious quantity. This is based on a talk given at IInd Recontre du Vietnam. However I have added some developments which took place very recently to make the article meaningful at this time. Even before the phenomenon of black hole radiation was discovered, Beckenstein [1] noticed a profound analogy between black holes in classical general relativity and the laws of thermodynamics. In particular he found that the surface gravity at the horizon of a black hole can be regarded as a temperature and the area of the horizon as an entropy. Hawking [2] showed that black holes radiate due to quantum effects with a temperature which is indeed proportional to the surface gravity and this gave a precise formula for the “BeckensteinHawking entropy” SHB which, for simplest black holes, read